Quantum fault tolerant protocols and quantum phases

Conventional quantum error correction largely consists of two pieces: one to maintain the coherence of encoded qubits and apply Clifford operations on them and the other to implement non-Clifford gates, although there is no fundamental reason for these to be separated. In this talk, I will review the construction of fault-tolerant protocols, namely topological codes, fracton models, Floquet codes, and triorthogonal codes, in relation to our understanding of quantum phases.